基于全变分和权重核范数最小化的图像去噪算法

Image Denoising Algorithm Based on Total Variation and Weight Nuclear Norm Minimization

针对权重核范数最小化算法不能有效保留图像边缘信息的问题,利用全变分的良好的保持边缘信息的能力,提出一种基于全变分和权重核范数最小化的噪声抑制算法。权重核范数最小化充分利用图像的非局部相似性,对由非局部相似性得到的相似块构成的矩阵的不同的奇异值进行不同程度的收缩,从而对图像成分和噪声成分进行有效分离。同时,对该矩阵进行全变分正则化约束,可以有效保留图像的边缘信息,在降噪的同时避免造成边缘模糊。实验结果表明,与权重核范数最小化方法相比,所提方法不仅对图像的噪声抑制效果更好,而且得到的图像边缘清晰度更高。

Aiming at the problem that the weighted nuclear norm minimization algorithm cannot effectively preserve the information of image edge,a noise suppression algorithm based on total variation and weighted nuclear norm minimization is proposed by utilizing the good ability of preserving edge information of total variation.The weighted nuclear norm minimization makes full use of the non-local similarity of the image,and shrinks the different singular values of the matrix composed of similar blocks from non-local similarity to varying degrees,so as to effectively separate the image component from the noise component.At the same time,the matrix is constrained by total variation regularization,which can effectively preserve the edge information of the image and avoid blurring edges while reducing noise.The experimental results show that,compared with the weighted nuclear norm minimization method,the proposed method not only has better noise suppression effect on images,but also has higher edge sharpness.